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Question about the small arc method

constadin
Hello all!

Please let me know if I am doing something wrong following the small arc method.

Btw, I am using vector points and auto circles with NO CAD always in DCC mode. Let's also assume that I am measuring in Z plane.

1) I am measuring the small arc with a fixed radius auto circle.
2) I am setting my origin XY to this circle.
3) Just to be sure I am repeating with a new auto circle fixed radius and realign to it.
4) I am taking 3 vector points in polar coordinates to be precise.
5) I am reporting the PR of the points.

This morning I had a 80deg on an arc R2.8mm to measure. I used this method and I was getting repeatable results at 2.80. The issue is that the radius has been measured to be 2.75mm (verified with 2 other methods also).

I also tried to change the fixed rad value based on the R measurement I had performed before with least squares (around 2.75 non repeatable value) and I was getting results close to that value (the least square value).

With this method, does the fixed Radius value provided alter the centre that is being found? Doesn't this beat the purpose of using this method?

Thanks in advance!
  • Sorry, been very busy and not had chance to look in here much.

    From what you've said I believe you are doing it correctly, but this thread has given me cause to think more about this method. Before I comment more however if like to do a few tests (quite when I'll get a chance to do that is another question though!).
  • Good Day,

    As others have already said:
    With the T-Value or, in other words, with a surface profile, you get "repeatable" measurements.
    as long as your alignment is stable.

    maybe that's enough to decide if the area is in spec
  • Good Day,

    As others have already said:
    With the T-Value or, in other words, with a surface profile, you get "repeatable" measurements.
    as long as your alignment is stable.

    maybe that's enough to decide if the area is in spec


    Unfortunately not in my field and position. The data are put on a database and the checklist that contain the ⌀ measurement are already premade. Only a ⌀ measurement is accepted in this case and a PR of the points taken would be put in a created circle that would have ⌀= 2*PR of the point (or points actually).

    @ ​ thanks for the confirmation, I would be very interested to hear the results of your tests when you find the time to investigate!


  • I am not sure I follow. So you use the fix rad method to find a center or not? Not really sure how this can help in the issue I have with the accuracy of this method Disappointed
    If there is a "repeatable and accurate" way to measure small arcs other than going the least square methos, please someone list the steps because I am clearly missing something with the fix rad method.

    Yes I use the fixed radius method to find center. And then I take individual points on the radius and report out the deviation of the surface. Usually the customer prefers a single numerical value so I will create a feature set and report out the deviation of said FS (usually as a form only profile) but almost always include the individual point T values as well.

    Its something that I have done. it may not be entirely correct but I have never gotten reliable or repeatable results with the Polar Angle method so I use this method instead.
  • When using the fixed rad method, you really need to take an iterative approach. Think of how you would check a small, partial radius manually, using radius gauges. You would offer up a gauge and look for gaps, before trying progressively larger/smaller gauges until you were satisfied that the gauge fitted snugly into the radius with no visible gap anywhere. It's the same with the fixed rad method - when you fix the radius, this is like saying "I have a radius gauge of this size". PC-DMIS will give you the co-ordinates for the centre of that known diameter when it is in contact with the hits. You then origin on those co-ordinates and take additional polar radial points along the radius. Depending on the deviation you see for each hit, you would then need to adjust your fixed rad size and repeat.

    For example, suppose you had a partial radius going from 0° to 45° of arc whose theoretical size was Ø20. You would start by measuring a fixed rad circle (Ø20) with a reasonable spread of hits, covering as much of the arc as possible. You would then origin on that circle and take three polar radial hits, one at 0°, one at 22.5° (the middle of the arc) and one at 45°. Next, you would check the polar value of the hits. If the "middle" (22.5°) hit was larger than 10, it would indicate that the original fixed rad size was too large - think of what you would see if you were to offer up a radius gauge that was larger than the actual radius, you would see a gap near the middle of the arc. Similarly, if the polar value of your middle point was ~10 but the polar radial value for the other two hits (the ones at each end of the arc) were larger, it would indicate that your original fixed rad size was too small. Again, think of a radius gauge. A gauge that is smaller than the actual radius would contact in the middle but have a gap at each end of the arc. Based on this, you would measure another fixed rad circle, this time with the fixed rad size adjusted by some amount, origin on it and take another three polar radial hits. You would repeat this process until the polar radial values of all three hits were as close to each other as possible (you may need to increase the decimal precision) allowing for the accuracy of your CMM. You would then have both an accurate size and set of centre co-ordinates for the radius.

    Obviously, the smaller the degree of arc and the bigger the uncertainty statement for your CMM, the harder it will be to make this assessment, but the principle is sound. It can, however, be extremely time consuming and difficult to code up, relying on logical expressions and looping or many "trial and error" attempts. This is why most people feel it is generally better to report profile of a line / surface to determine whether the radius is acceptable.
  • When using the fixed rad method, you really need to take an iterative approach. Think of how you would check a small, partial radius manually, using radius gauges. You would offer up a gauge and look for gaps, before trying progressively larger/smaller gauges until you were satisfied that the gauge fitted snugly into the radius with no visible gap anywhere. It's the same with the fixed rad method - when you fix the radius, this is like saying "I have a radius gauge of this size". PC-DMIS will give you the co-ordinates for the centre of that known diameter when it is in contact with the hits. You then origin on those co-ordinates and take additional polar radial points along the radius. Depending on the deviation you see for each hit, you would then need to adjust your fixed rad size and repeat.

    For example, suppose you had a partial radius going from 0° to 45° of arc whose theoretical size was Ø20. You would start by measuring a fixed rad circle (Ø20) with a reasonable spread of hits, covering as much of the arc as possible. You would then origin on that circle and take three polar radial hits, one at 0°, one at 22.5° (the middle of the arc) and one at 45°. Next, you would check the polar value of the hits. If the "middle" (22.5°) hit was larger than 10, it would indicate that the original fixed rad size was too large - think of what you would see if you were to offer up a radius gauge that was larger than the actual radius, you would see a gap near the middle of the arc. Similarly, if the polar value of your middle point was ~10 but the polar radial value for the other two hits (the ones at each end of the arc) were larger, it would indicate that your original fixed rad size was too small. Again, think of a radius gauge. A gauge that is smaller than the actual radius would contact in the middle but have a gap at each end of the arc. Based on this, you would measure another fixed rad circle, this time with the fixed rad size adjusted by some amount, origin on it and take another three polar radial hits. You would repeat this process until the polar radial values of all three hits were as close to each other as possible (you may need to increase the decimal precision) allowing for the accuracy of your CMM. You would then have both an accurate size and set of centre co-ordinates for the radius.

    Obviously, the smaller the degree of arc and the bigger the uncertainty statement for your CMM, the harder it will be to make this assessment, but the principle is sound. It can, however, be extremely time consuming and difficult to code up, relying on logical expressions and looping or many "trial and error" attempts. This is why most people feel it is generally better to report profile of a line / surface to determine whether the radius is acceptable.

    This explanation is brilliant, thanks a lot! As a side note, this pdf you guys released should seriously be adjusted to include all this info...
  • Hi,

    Using the small arc method, I measured a small radius of 3.18mm on a part, but I wrongly set the fixed rad value as 4.57mm (instead of 3.18) and when displaying PR results it shows around 4.57mm. (using auto hits after fixed rad alignment)

    I'm confused now.
  • Hi,
    It's because you settled the alignment at 4.57 of the surface...
    So you shouldn't get the right compensation, and the PR (polar radius) is calculated from the origin.
    No kind of magic here for me Slight smile.
  • This is how I deal with it, with yours 3 points ( more points, the better)

    1. Create polar vectors points
    2. ASSIGN/AVG=SUM(PNT1.PR,M+PNT2.PR.M+PNT3.PR.M)/3
    3. create Generic point
    MEAS/XYZ,<AVG,Y,Z)
    4. Report GENERIC point

  • theoretical center is more estimation than measurement the smaller arc and radius are

    you can take 10 pieces from different days of production and you will see they are all different you will find differences with your eye no need any profile or microscope for this :)  

    i spend lot of time with alignments on ~~ R1  arcs, with tip 1mm calibrated on ~~0.003 mm it was not accurate enough 

    When you take any 3 points on some arc drawn in CAD you always have same results, but make one point of arc moved 0.01mm and see your results, then move it along the arc few times

    While see small arcs on profile testers  you find out they have roundness, waviness, roughness, they are always rotated around its TED center, more if are smaller 

    While measuring R0.2mm sometimes you can say "its not even a part of circle" its just some parabolic shape or what ... 

    I saw measurement of R0.7 but it was never few points 

    in my opinion need accurate machine to measure small radius with small angular coverage, use always smallest probe you can, take as much points like profile tester - not 10 but 1000 5000 because your machine needs some data for least squares method calculation and for filtering surfaces and measurement errors , and do it like on profile tester - scan not only arc but surfaces close to it so you can choose and decide (even with every single measurement)  witch points you consider as circle and what are rather part of surrounding planes. 

    Or just do it on profile tester its usually better, because some things need just too much luck do be done 

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